When I connect the 4K Ultra HD BRAVIA TV to the PlayStation 4 Pro, 4K HDR is not recognized on Video Output Settings.

Only 2K supported is displayed for HDR on Your TV in Video Output Information of the PlayStation 4 Pro.

Check the following.

Check the HDMI cable used for connecting the BRAVIA TV and the PlayStation 4 Pro. Check if the cable is the HDMI cable supplied with the PlayStation 4 Pro or the Premium high speed HDMI cable which supports 18 Gbps.

Confirm that an HDMI terminal on the BRAVIA TV supports HDR. Depending on the model, only some HDMI terminals may support HDR. For details, refer to the following Q&A.Is my BRAVIA TV compatible with HDR?

Set HDMI signal format to Enhanced format on the BRAVIA TV.

Press the HOME button on the remote control.

Select Settings.

Select External inputs in the TV category.

Select HDMI signal format and set to Enhanced format.

Set the HDR to Automatic on the PlayStation 4 Pro.

Press the PS button on the controller of the PlayStation 4 Pro to display the HOME screen.

Select Settings.

Select Sound and Screen.

Select Video Output Settings.

Set HDR to Automatic.

If there is no problem in the steps so far, the PlayStation 4 Pro can output the HDR signal to the BRAVIA TV, but the settings of the PlayStation 4 Pro cannot be correctly reflected to the BRAVIA TV.Please confirm that Video Output settings in the PlayStation 4 Pro is indicated correctly by following the procedure below.

Press the PS button on the controller of the PlayStation 4 Pro to display the HOME screen.NOTE: When Video Output Settings has been already displayed, be sure to perform this procedure once.

Confirm that the settings are recognized correctly by following the procedure below. For Resolution

Select Settings.

Select Sound and Screen.

Select Video Output Settings.

Select Resolution, then check if 2160p-RGB can be selected .

For HDR on Your TV

Select Settings.

Select Sound and Screen.

Select Video Output Settings.

Select Video Output Information.

Select HDR on Your TV, then check if 2K/4K Supported is displayed.

If the issue is not resolved, update the system software of your Playstation 4 Pro to the latest version.